FROSTING: Put the confectioner’s sugar in a food processor along with the butter, salt and vanilla; process until creamy and fully combined, 30-45 seconds. With the processor running, gradually add enough cream of coconut to reach a spreadable consistency.

When the cake is cool, put the first layer, top side down, on a plate or cake stand. Spread a third of the frosting on top, all the way to the edges, and sprinkle with 3/4 cup shredded coconut. Put the other layer on top, flat side down. Spread on another third of the frosting, and use the rest to cover the sides. Press the remaining coconut onto the top and sides of the cake. Cover with wax paper, and store at room temperature for up to 2 days; covered with plastic wrap, it will last an extra day.
* Cream of coconut is available in the liquor section of most supermarkets.